Problem: The grades on a math midterm at Springer are normally distributed with $\mu = 68$ and $\sigma = 4.5$. Brandon earned a $71$ on the exam. Find the z-score for Brandon's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Brandon's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{71 - {68}}{{4.5}}} $ ${ z \approx 0.67}$ The z-score is $0.67$. In other words, Brandon's score was $0.67$ standard deviations above the mean.